5.5.2. MIQP Modeling and Optimization in CΒΆ
In this chapter, we will use MindOpt C API to model and solve the problem in Example of Mixed Integer Quadratic Programming.
First of all, include the header files:
29#include "Mindopt.h"
Create an optimization model m:
93 /*------------------------------------------------------------------*/
94 CHECK_RESULT(MDOemptyenv(&env));
95 CHECK_RESULT(MDOstartenv(env));
Next, we set the optimization sense to minimization via MDOsetintattr() and add four decision variables using MDOaddvar() (please refer to C API for more detailed usages of C API):
105 /* Add variables. */
106 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 1.0, 0, 10.0, MDO_INTEGER, "x0"));
107 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 2.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x1"));
108 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x2"));
Now we set the constraint matrix \(A\) following the same procedure as in LP. The arrays row1_idx and row2_idx represent positions of the non-zero elements in the first and second rows while row1_val and row2_val represent corresponding values of the non-zero elements.
68 */
69 int qo_col1[] =
70 {
71 0,
72 1, 1,
73 2,
74 3
75 };
76 int qo_col2[] =
77 {
78 0,
79 0, 1,
80 2,
81 3
82 };
83 double qo_values[] =
84 {
85 1.0,
86 0.5, 1.0,
87 1.0,
88 1.0
We call MDOaddconstr() to input the linear constraints into the model m:
68 */
69 int qo_col1[] =
70 {
71 0,
72 1, 1,
73 2,
74 3
75 };
76 int qo_col2[] =
77 {
78 0,
79 0, 1,
80 2,
81 3
82 };
83 double qo_values[] =
84 {
85 1.0,
86 0.5, 1.0,
87 1.0,
88 1.0
Next, we will introduce the quadratic terms in the objective. Three arrays are utilized for this purpose. Specifically, qo_col1, qo_col2, and qo_values record the row indices, column indices, and values of all the non-zero quadratic terms.
110 /* Add constraints.
Once the model is constructed, we call MDOoptimize() to solve the problem:
116 /* Add quadratic objective term. */
Then, we can retrieive the optimal objective value and solutions as follows:
128 /* For MIP(MILP,MIQP, MIQCP) problems, if the solving process */
129 /* terminates early due to reasons such as timeout or interruption, */
130 /* the model status will indicate termination by timeout (or */
131 /* interruption, etc.). However, suboptimal solutions may still */
132 /* exist, making it necessary to check the SolCount property. */
133 /*------------------------------------------------------------------*/
134 CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
135 CHECK_RESULT(MDOgetintattr(m, SOL_COUNT, &solcount));
136 if (status == MDO_OPTIMAL || status == MDO_SUB_OPTIMAL || solcount != 0)
137 {
Lastly, we call MDOfreemodel() and MDOfreeenv() to free the model:
30/* Macro to check the return code */
31#define RELEASE_MEMORY \
146 else
Complete example codes are provided in MdoMIQPEx1.c.
1/**
2 * Description
3 * -----------
4 *
5 * Mixed Integer Quadratic optimization (row-wise input).
6 *
7 * Formulation
8
9 * -----------
10 *
11 * Minimize
12 * obj: 1 x0 + 1 x1 + 1 x2 + 1 x3
13 * + 1/2 [ x0^2 + x1^2 + x2^2 + x3^2 + x0 x1]
14 * Subject To
15 * c0 : 1 x0 + 1 x1 + 2 x2 + 3 x3 >= 1
16 * c1 : 1 x0 - 1 x2 + 6 x3 = 1
17 * Bounds
18 * 0 <= x0 <= 10
19 * 0 <= x1
20 * 0 <= x2
21 * 0 <= x3
22 * Integers
23 * x0
24 * End
25 */
26
27#include <stdio.h>
28#include <stdlib.h>
29#include "Mindopt.h"
30
31/* Macro to check the return code */
32#define RELEASE_MEMORY \
33 MDOfreemodel(model); \
34 MDOfreeenv(env);
35#define CHECK_RESULT(code) { int res = code; if (res != 0) { fprintf(stderr, "Bad code: %d\n", res); RELEASE_MEMORY; return (res); } }
36#define MODEL_NAME "MIQCP_01"
37#define MODEL_SENSE "ModelSense"
38#define SOL_COUNT "SolCount"
39#define STATUS "Status"
40#define OBJ_VAL "ObjVal"
41#define X "X"
42
43int main(void)
44{
45 /* Variables. */
46 MDOenv *env;
47 MDOmodel *model;
48 double obj, x;
49 int i, solcount, status;
50
51 /* Model data. */
52 int row1_idx[] = { 0, 1, 2, 3 };
53 double row1_val[] = { 1.0, 1.0, 2.0, 3.0 };
54 int row2_idx[] = { 0, 2, 3 };
55 double row2_val[] = { 1.0, -1.0, 6.0 };
56
57 /* Quadratic objective matrix Q.
58 *
59 * Note.
60 * 1. The objective function is defined as c^Tx + 1/2 x^TQx, where Q is stored with coordinate format.
61 * 2. Q will be scaled by 1/2 internally.
62 * 3. To ensure the symmetricity of Q, user needs to input only the lower triangular part.
63 *
64 * Q = [ 1.0 0.5 0 0 ]
65 * [ 0.5 1.0 0 0 ]
66 * [ 0.0 0.0 1.0 0 ]
67 * [ 0 0 0 1.0 ]
68 */
69 int qo_col1[] =
70 {
71 0,
72 1, 1,
73 2,
74 3
75 };
76 int qo_col2[] =
77 {
78 0,
79 0, 1,
80 2,
81 3
82 };
83 double qo_values[] =
84 {
85 1.0,
86 0.5, 1.0,
87 1.0,
88 1.0
89 };
90
91 /*------------------------------------------------------------------*/
92 /* Step 1. Create environment and model. */
93 /*------------------------------------------------------------------*/
94 CHECK_RESULT(MDOemptyenv(&env));
95 CHECK_RESULT(MDOstartenv(env));
96 CHECK_RESULT(MDOnewmodel(env, &model, MODEL_NAME, 0, NULL, NULL, NULL, NULL, NULL));
97
98
99 /*------------------------------------------------------------------*/
100 /* Step 2. Input model. */
101 /*------------------------------------------------------------------*/
102 /* Change to minimization problem. */
103 CHECK_RESULT(MDOsetintattr(model, MODEL_SENSE, MDO_MINIMIZE));
104
105 /* Add variables. */
106 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 1.0, 0, 10.0, MDO_INTEGER, "x0"));
107 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 2.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x1"));
108 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x2"));
109 CHECK_RESULT(MDOaddvar(model, 0, NULL, NULL, 1.0, 0, MDO_INFINITY, MDO_CONTINUOUS, "x3"));
110
111 /* Add constraints.
112 * Note that the nonzero elements are inputted in a row-wise order here.
113 */
114 CHECK_RESULT(MDOaddconstr(model, 4, row1_idx, row1_val, MDO_GREATER_EQUAL, 1.0, "c0"));
115 CHECK_RESULT(MDOaddconstr(model, 3, row2_idx, row2_val, MDO_EQUAL, 1.0, "c1"));
116
117 /* Add quadratic objective term. */
118 CHECK_RESULT(MDOaddqpterms(model, 5, qo_col1, qo_col2, qo_values));
119
120 /*------------------------------------------------------------------*/
121 /* Step 3. Solve the problem and populate optimization result. */
122 /*------------------------------------------------------------------*/
123 /* Solve the problem. */
124 CHECK_RESULT(MDOoptimize(model));
125
126 /*------------------------------------------------------------------*/
127 /* Step 4. Retrive model status and objective. */
128 /* For MIP(MILP,MIQP, MIQCP) problems, if the solving process */
129 /* terminates early due to reasons such as timeout or interruption, */
130 /* the model status will indicate termination by timeout (or */
131 /* interruption, etc.). However, suboptimal solutions may still */
132 /* exist, making it necessary to check the SolCount property. */
133 /*------------------------------------------------------------------*/
134 CHECK_RESULT(MDOgetintattr(m, STATUS, &status));
135 CHECK_RESULT(MDOgetintattr(m, SOL_COUNT, &solcount));
136 if (status == MDO_OPTIMAL || status == MDO_SUB_OPTIMAL || solcount != 0)
137 {
138 CHECK_RESULT(MDOgetdblattr(model, OBJ_VAL, &obj));
139 printf("The optimal objective value is: %f\n", obj);
140 for (int i = 0; i < 4; ++i)
141 {
142 CHECK_RESULT(MDOgetdblattrelement(model, X, i, &x));
143 printf("x[%d] = %f\n", i, x);
144 }
145 }
146 else
147 {
148 printf("No feasible solution.\n");
149 }
150
151 /*------------------------------------------------------------------*/
152 /* Step 4. Free the model. */
153 /*------------------------------------------------------------------*/
154 RELEASE_MEMORY;
155
156 return 0;
157}